Any deal that could be struck for Sancho is separate to the one being negotiated between PSG and United for Argentinian midfielder Manuel Ugarte.
RMC Sport say that Sancho, 25, is 'interested in joining the Parisian club', but United would only let him leave if PSG meet their asking price of around £51million.
It comes after Erik Ten Hag had revealed new plans for the £77m star last week, with the Dutchman stating that the England forward could play more centrally as a No 9 in the Dutchman's front three.
'Jadon can, of course, play as a striker,' Ten Hag said, when asked on his position.
Erik Ten Hag had revealed new plans for the £77m star last week, with the Dutchman stating that the England forward could play more centrally as a No 9
Sancho has featured in five of United's opening six pre-season matches, coming off the bench during their FA Community Shield defeat by Manchester City on Saturday afternoon.
Sancho would subsequently step up to take a penalty in the resulting shoot-out, but missed his spot-kick.
But Ten Hag once again delivered the backing to his winger, stating: 'He’s a very good penalty taker and I had — and have — no doubts to let him score a penalty. Also in the future, he will take penalties.'
The pair appear to have set aside any previous tensions after the winger left the club midway through last season, following a spat with the Dutchman.
Ten Hag had criticised Sancho for his work rate in training, comments that the winger took unkindly to, calling the football coach out on social media, claiming that he had lied - and subsequently refused to apologise for the statement, leading to his exile from the club.
He joined Dortmund midway through the 2023-24 season but has since returned to United.
'We spoke well,' Ten Hag said on his relationship with Sancho. 'Anyone can make a mistake. If the player reflects well on that, then draw a line and continue again.
'This club needs good players, and one thing is for sure: Jadon Sancho is a terribly good player. I hope the click will come after all, and that it will contribute to our success.'
United have, meanwhile, been looking into a deal to sign Ugarte from PSG, but had been unwilling to meet French club's £52m asking price.
United today confirmed their third and fourth signings of the transfer window after completing a £60m double swoop for Matthijs de Ligt and Noussair Mazraoui. They'll join Joshua Zirkzee and Leny Yoro as new arrivals this summer with United having spent around £149m.